Question 1

Find the distance between the given point Q and the given line.
-Q(-9, 1, 10); x = -5 + 3t, y = 1 - t, z = 7 + 4t

Accepted Answer

A)  6  
B)  5  
C)  5 
D)  6

Question 2

Express the vector in the form ai + bj.
- if  is the point ( 2, -6) and  is the point ( 4, -9)

Accepted Answer

A)  v = -i + 3j 
B)  v = 2i - 3j 
C)  v = -2i + 3j 
D)  v = -2i - 3j

Question 3

Find v ∙ u.
-v = 5i + 4j and u = 2i + 6j

Accepted Answer

A)  34 
B)  7i + 10j 
C)  -14 
D)  10i + 24j

Question 4

Write the equation for the plane.
-The plane through the points P( 5, -3, -1) , Q( -3, 5, -33) and R( -1, 4, -32).

Accepted Answer

A)  7x + y + 3z = 7 
B)  7x + y + 3z = -7 
C)  3x + 7y + z = -7 
D)  3x + 7y + z = 7

Question 5

Write the equation for the plane.
-The plane through the point P( 2, 2, 7) and normal to n =

Accepted Answer

A)  2x + 2y - 7z = -16 
B)  4x + 3y - 2z = -16 
C)  -4x - 3y + 2z = 0 
D)  -2x - 2y + 7z = -16

Question 6

Find u.  
-v = 2i - 2j - 4k, u = 12i - 5k

Accepted Answer

A)  
 
B)  
 
C)  
 
D)

Question 7

Find u.  
-v = k, u = 6i + 9j + 2k

Accepted Answer

A)  
 
B)  
 
C)  
 
D) 2k

Question 8

Determine whether the following is always true or not always true. Given reasons for your answers.
-(u × v) ∙ v = u ∙ (u × v)

Accepted Answer

The answer of Determine whether the following is always true...

Question 9

Solve the problem.
-A bullet is fired with a muzzle velocity of 1159 ft/sec from a gun aimed at an angle of 29° above the horizontal. Find the horizontal component of the velocity.

Accepted Answer

A)  1014 ft/sec 
B)  -867.0 ft/sec 
C)  561.9 ft/sec 
D)  642.4 ft/sec

Question 10

Find the indicated vector.
-Let u =  , v =  . Find  u +  v.

Accepted Answer

A)   
B)   
C)   
D)

Question 11

Identify the type of surface represented by the given equation.
- -  =

Accepted Answer

A)  Paraboloid 
B)  Parabolic cylinder 
C)  Hyperbolic paraboloid 
D)  Ellipsoid

Question 12

Find u.  
-v = 3i - j + 3k, u = 11i + 2j + 10k

Accepted Answer

A)  
 
B)  
 
C)  
 
D)

Question 13

Find the intersection.
--4x - 3y + 9z = 10, 6x - 8y + 2z = -2

Accepted Answer

A)  x = 66t + 86, y = 62t - 52, z = -50t 
B)  x = 3300t + 86, y = 3100t + 52, z = -50t 
C)  x = -66t - 86, y = -62t + -52, z = -50t 
D)  x = 66t -  , y = 62t -  , z = 50t

Question 14

Find the indicated vector.
-Let u =  . Find -8u.

Accepted Answer

A)   
B)   
C)   
D)

Question 15

Find v ∙ u.
-v = 3i - 7j and u = -3  i + 7j

Accepted Answer

A)  ( 3 - 3  )i + 0j 
B)  -49 - 9  
C)  -49  i - 9j 
D)  -49  + 9

Question 16

Identify the quadric surface by name. Find and describe the xy-, xz-, and yz-traces, when they exist.
--9  - 9  +  = 9

Accepted Answer

A)   Ellipsoid; xy-trace: -9xS1U1P12S1S1P0  - 9yS1U1P12S1S1P0  = 9 (circle); xz-trace: zS1U1P12 S1S1P0 - 9 xS1U1P12S1S1P0  = 9 (ellipse); yz-trace:  zS1U1P12S1S1P0 - 9 yS1U1P12S1S1P0 = 9 (ellipse) 
B)   Hyperboloid of two sheets; xy-trace: -9xS1U1P12S1S1P0  - 9yS1U1P12S1S1P0  = 9(circle); xz-trace: zS1U1P12 S1S1P0 - 9 xS1U1P12S1S1P0  = 9 (hyperbola); yz-trace:   zS1U1P12 S1S1P0 - 9 yS1U1P12S1S1P0  = 9 (hyperbola) 
C)   Hyperboloid of two sheets; xz-trace: zS1U1P12 S1S1P0 - 9 xS1U1P12S1S1P0  = 9 (hyperbola); yz-trace:  zS1U1P12 S1S1P0 - 9 yS1U1P12S1S1P0  = 9(hyperbola) 
D)   Hyperboloid of one sheet; xy-trace: -9xS1U1P12S1S1P0  - 9yS1U1P12S1S1P0  = 9 (circle); xz-trace:  zS1U1P12 S1S1P0 - 9 yS1U1P12S1S1P0  = 9 (hyperbola); yz-trace: zS1U1P12S1S1P0  - 9yS1U1P12S1S1P0  = 9 (hyperbola)

Question 17

Solve the problem.
-How much work does it take to slide a box 6 meters along the ground by pulling it with a 158 N force at an angle of 15° from the horizontal?

Accepted Answer

A)  915.7 joules 
B)  -720.2 joules 
C)  152.6 joules 
D)  948 joules

Question 18

Use a calculator to find the acute angle between the planes to the nearest thousandth of a radian.
-8x + 6y + 6z = -3 and 10x + 9y + 3z = -8

Accepted Answer

A)  1.446 rad 
B)  0.331 rad 
C)  1.521 rad 
D)  1.239 rad

Question 19

Find the triple scalar product (u x v) ∙ w of the given vectors.
-u = i + j + k; v = 8i + 5j + 2k; w = 9i + 6j + 4k

Accepted Answer

A)  -9 
B)  25 
C)  75 
D)  -3

Question 20

Write the equation for the plane.
-The plane passing through the point P0(-3, 1, 7) that is perpendicular to the line x = -1 + 6t, y = 2 - 5t,

Accepted Answer

A)  6x - 5y + 4z = 5 
B)  -3x + y + 7z = 68 
C)  4x + 9y + 2z = 11 
D)  -x + 2y + 3z = 26

Exam 13: Vectors and the Geometry of Space

Find the distance between the given point Q and the given line. -Q(-9, 1, 10) ; x = -5 + 3t, y = 1 - t, z = 7 + 4t

Express the vector in the form ai + bj. - if is the point ( 2, -6) and is the point ( 4, -9)

Find v ∙ u. -v = 5i + 4j and u = 2i + 6j

Write the equation for the plane. -The plane through the points P( 5, -3, -1) , Q( -3, 5, -33) and R( -1, 4, -32) .

Write the equation for the plane. -The plane through the point P( 2, 2, 7) and normal to n =

Find u. -v = 2i - 2j - 4k, u = 12i - 5k

Find u. -v = k, u = 6i + 9j + 2k

Determine whether the following is always true or not always true. Given reasons for your answers. -(u × v) ∙ v = u ∙ (u × v)

Solve the problem. -A bullet is fired with a muzzle velocity of 1159 ft/sec from a gun aimed at an angle of 29° above the horizontal. Find the horizontal component of the velocity.

Find the indicated vector. -Let u = , v = . Find u + v.

Identify the type of surface represented by the given equation. - - =

Find u. -v = 3i - j + 3k, u = 11i + 2j + 10k

Find the intersection. --4x - 3y + 9z = 10, 6x - 8y + 2z = -2

Find the indicated vector. -Let u = . Find -8u.

Find v ∙ u. -v = 3i - 7j and u = -3 i + 7j

Identify the quadric surface by name. Find and describe the xy-, xz-, and yz-traces, when they exist. --9 - 9 + = 9

Solve the problem. -How much work does it take to slide a box 6 meters along the ground by pulling it with a 158 N force at an angle of 15° from the horizontal?

Use a calculator to find the acute angle between the planes to the nearest thousandth of a radian. -8x + 6y + 6z = -3 and 10x + 9y + 3z = -8

Find the triple scalar product (u x v) ∙ w of the given vectors. -u = i + j + k; v = 8i + 5j + 2k; w = 9i + 6j + 4k

Write the equation for the plane. -The plane passing through the point P₀(-3, 1, 7) that is perpendicular to the line x = -1 + 6t, y = 2 - 5t,